The present invention generally relates to digital-to-analog converting devices, and more particularly to a digital-to-analog converting device which converts a discrete digital signal into an analog signal having a continuous amplitude with substantially no deterioration in the signal quality.
Recently, there has been a rapid progress in large scale integrated (LSI) circuit techniques, and the rapid progress is particularly notable in digital LSI circuit techniques. With such technical progress in these fields, precision of circuit elements has improved, and it is becoming possible to downsize circuit devices and reduce the manufacturing cost of the circuit devices. For this reason, it is becoming more popular to subject an analog information signal to a digital signal processing, especially when transmitting an audio signal. That is, the analog information signal is subjected to a digital pulse modulation such as a pulse code modulation (PCM) and converted into a digital signal format to be transmitted through a transmitting medium or to be processed, and the digital signal is thereafter restored to the original analog information signal. Such a digital signal processing technique is applied to various devices, and reduced to practice.
As is well known, a high signal-to-noise (S/N) ratio can be obtained according to the above digital signal processing system. Moreover, it is possible to obtain a large dynamic range. In addition, the signal quality will not become deteriorated if sufficiently long data words and operation words are reserved when transmitting and processing a signal through the transmitting medium. These advantageous features help prevent the signal quality from being deteriorated, especially when transmitting a high-quality music signal through a recording medium such as a tape and a disc, changing the sound quality of the music signal frequently a plurality of times, and carrying out a signal processing such as mixing of the music signal with other signals. Thus, it is particularly suited to apply these digital signal processing in transmission of an audio signal. Accordingly, attention is recently being drawn towards digital audio systems, and a digital audio disc (DAD) for home use has already been reduced to practice.
However, even in the digital processing system, conventional analog circuits are used in input and output circuits, to carry out conversion of an analog signal into a digital signal and vice versa. That is, an analog-to-digital (A/D) converter is required for converting an input analog signal into a digital signal x.sub.n having a predetermined data word length (number of bits) n, and a digital-to-analog (D/A) converter is required for limiting a digital signal y.sub.n to a predetermined word length and for converting the digital signal y.sub.n into an analog signal. Because these converting processes involve the A/D converter and D/A converter which have resolutions of predetermined data word lengths, noise due to error between the analog signal and the quantized signal, that is, quantization noise is inevitably introduced by the conversion.
If the original analog signal is in the low frequency range, the quantization noise called granular noise is generated in the A/D converter because the quantization level is limited. In addition, if the level of the original analog signal is low (if the effective data word length is short in the case of a digital signal), the otuput signal waveform becomes a square wave when the original analog signal is sampled. This output signal includes much harmonic distortion, and the harmonic distortions may be detected by the listener as an unpleasant sound or noise.
Such noise was a substantial problem in the digital audio system in which the signal quality was of much importance. That is, in the digital audio system, the PCM digital music signal is subjected to change in the sound quality in a variable attenuation equalizer and the like, or subjected to a mixing process, and the operation word length is normally set longer than the data word length of the signal to reduce the operation error in order to prevent the signal quality from being deteriorated when carrying out such a process. However, although the input digital signal y.sub.n of the D/A converter has a sufficiently long data word length, quantization noise is generated due to truncation of the data word length of the input digital signal of the D/A converter, because the resolution of the D/A converter is limited to the predetermined number of bits.
In addition, in order to obtain a wide passband in accordance with the sampling theorem, a passband edge frequency or passband cutoff frequency f.sub.p of an analog lowpass filter connected to the output of the D/A converter is set to a frequency which is exceedingly close to a stopband edge frequency or stopband cutoff frequency f.sub.s of the analog lowpass filter. Further, the above frequencies f.sub.p and f.sub.s satisfy a relation f.sub.p &lt;f.sub.s .ltoreq.F.sub.s /2, where F.sub.s is the sampling frequency of the output digital signal of the D/A converter. Hence, the above analog lowpass filter has a characteristic in which a transition frequency band between the passband edge frequency f.sub.p and the stopband edge frequency f.sub.s is narrow, that is, the transition between the passband edge frequency f.sub.p and the stopband edge frequency f.sub.s is sharp.
For example, when transmitting an audio signal, the transition band is only about 5 kHz, since the passband edge frequency f.sub.p is in the range of 20 kHz and the sampling frequency f.sub.1 is in the range of 50 kHz. On the other hand, the attenuation or loss of the analog lowpass filter corresponds to the quantization bit number of the digital signal, and an attenuation of -96 dB is required when the quantization bit number is 16. Accordingly, the attenuation characteristic of the analog lowpass filter must be extremely sharp, that is, the transition between the passband edge frequency and the stopband edge frequency must be sharp, and conventionally, an elliptic filter having its order of the filter in the range of 11 to 13 was designed and used in most cases.
However, because the attenuation characteristics must be extremely sharp as described above, it was difficult to obtain a desired attenuation due to the precision of circuit elements. In addition, deviation from designed values had to be tolerated with, and the generation of ripple within the passband had to be tolerated with in order to obtain the desired attenuation. Further, the scale of the filter became large. Therefore, various problems were introduced in designing and making the analog lowpass filter. Moreover, if an attempt was made to obtain a sharp attenuation characteristic, the phase versus frequency characteristic of the analog lowpass filter inevitably became a characteristic in which the phase greatly varies in a range of +.pi.(radians) within the passband below the pasband edge frequency f.sub.p, for example, and it was impossible to suppress such great phase variation. Accordingly, there was a serious disadvantage in that the signal quality of the converted analog signal especially with respect to its phase became deteriorated.
In addition, even when the A/D converter and the D/A converter use 16 bits, it has been found that the actual performance of the converters was in the range of 14.5 bits. Thus, the fundamental performance of the converters were not being sufficiently obtained.
Hence, various methods were heretofore employed in order to reduce the quantization noise. For example, the resolution or number of bits of the D/A converter as increased by using the existing LSI technique. As another example, there was a method of constantly varying the minimum quantization level (the magnitude of the least significant bit) according to the signal characteristic so as to increase the apparent quantization word length, such as companded quantization or polygoral line quantization.
Furthermore, there was a method of reducing the quantization noise by use of white noise called dither. According to this method, a first white noise is superimposed to the analog signal and the superimposed signal was supplied to an A/D converter. A digital signal obtained from this A/D converter was then passed through a transmitting medium and a D/A converter, to obtain an analog signal in which the white noise is superimposed. A second white noise generated independently, was subtracted from the output analog signal of this D/A converter, to obtain the original analog signal. Thus, the quantization nosie was subjected to noise variance, and the distortion component was reduced.
In addition, there was a device for carrying out D/A conversion at twice the normal speed by inserting a digital filter at a stage preceding the D/A converter and converting the sampling frequency of twice the normal sampling frequency, in order to eliminate the various problems of the analog lowpass filter which is connected to the output side of the D/A converter. According to this device, the construction of the analog lowpass filter was simplified by effectively using the digital fitler which is easily designed to have a certain performance, and facilitated the designing and making of the analog lowpass filter. Moreover, it was possible to improve the signal quality of the analog signal (video signal, for example) which has passed through the filter. Thus, this device was effective when applied to a system in which the phase characteristic became a problem (refer to "Digital Interpolation System in A/D and D/A Conversion" by Ninomiya, NHK Technical Report, October 1979, page 405).
However, among the above methods of reducing the quantization noise employed heretofore, it would be easier to speed up the conversion time, for example, than employ the method of increasing the resolution of the D/A converter. This is because a D/A converter having a resolution of 16 bits has already been reduced to practice in the digital audio system in which there is a demand for signal transmission of particularly high quality, and from the point of circuit precision, circuit stability, and cost, it is difficult to further increase the resolution of the D/A converter. In addition, regarding the method of reducing the quantization noise by a non-linear quantization such as companded quantization, the noise is not substantially reduced because the quantization level is high at points where the signal level is high. Moreover, there is a problem in that the quantization noise such as granular noise is not reduced satisfactorily.
The method of reducing the quantization noise by use of the dither worked on the premise that the a first dither generator for generating the first white noise and a second dither generator for generating the second white noise are synchronized, and that a subtracting circuit carries out the subtraction of the second white noise from the analog signal in which the first white noise is superimposed. Thus, this method suffered a disadvantage in that the system became complex. When a recording medium such as a tape and disc was used, there were further disadvantages in that difficulty was introduced in obtaining compatibility with conventional systems because of the need to assure synchronism, that additional circuit systems were required, and the like. In a system in which the mixed dither cannot be subtracted, a method of simply adding noise and carrying out quantization was known in the case of video processing. However, the effect of noise variance could not be obtained unless the amplitude of the noise (dither) was large compared to the minimum quantization level. It is also known for the case of the audio signal that the noise increases and the S/N ratio becomes poor according to the input signal level, when such noise variance effect cannot be obtained. Therefore, there were problems in that the frequency of the noise which is added entered within the signal frequency band to cause deterioration of the signal quality, and that it was not practical to use noise having a frequency outside the signal frequency band.
On the other hand, in the conventional device in which the digital filter is inserted in a stage preceding the D/A converter and the sampling frequency is set to twice the normal sampling frequency so as to facilitate the design of the analog lowpass filter, it was necessary to increase the number of bits of the D/A converter by one when designing the digital filter. In addition, when designing the analog lowpass filter, measures had to be taken to attenuate the level increase caused by the increase by one bit, and this made it difficult to design the filter.
Further, a so-called noise shaping is known, according to which the quantization error is inverted with respect to the input digital signal and fed back to a stage preceding the D/A converter (for example, refer to Philips Technical Review 40, pp174-179, 1982, No. 6). However, the feedback cannot respond quick enough with respect to the high-frequency signal according to this method, and a type of over load noise is introduced. For example, the resolution increases by one bit when the digital signal is varying within a minimum quantization level .DELTA., however, the signal close to the quantization value (.DELTA., 2.DELTA.) passes unchanged. Thus, the quantization error becomes close to zero, and the feedback quantity becomes equal to zero, which means that the output value becomes equal to the value of the quantization level. Accordingly, the response of the signal which is obtained by passing the above signal through the D/A converter and the analog lowpass filter with respect to a rapidly rising signal (high-frequency signal) becomes poor. Therefore, there was a problem in that the effect of cancelling the quantization error with respect to the high-frequency range signal was poor, because the over load noise is introduced.